\[ \begin{array}{l} 4 x-2 y=7 \\ 7 x+2 y=15 \end{array} \] For the solution $(x, y)$ to the system of equations shown above, what is the value of $\frac{x}{y}$ ? A) $\frac{1}{2}$ B) $\frac{1}{4}$ C) 2 D) 4

Step 1 ：The system of equations is given by: \[\begin{array}{l} 4x - 2y = 7 \\ 7x + 2y = 15 \end{array}\]

Step 2 ：We can solve this system by adding the two equations together, which will eliminate the $y$ variable and allow us to solve for $x$.

Step 3 ：The solution to the system of equations is \(x = 2\) and \(y = \frac{1}{2}\).

Step 4 ：We are asked to find the value of \(\frac{x}{y}\). Substituting the values of $x$ and $y$ we found, we get \(\frac{x}{y} = \frac{2}{\frac{1}{2}} = 4\).

Step 5 ：Final Answer: The value of \(\frac{x}{y}\) is \(\boxed{4}\).